predictive capability evaluation of rsm and ann in ...complications like global warming, pollution,...

International Journal of Applied Engineering Research ISSN 0973-4562 Volume 13, Number 10 (2018) pp. 7529-7540

© Research India Publications. http://www.ripublication.com

7529

Predictive Capability Evaluation of RSM and ANN in Modeling and

Optimization of Biodiesel Production from Palm (Elaeisguineensis) Oil

Dang Nguyen Thoai1,2,*, Chakrit Tongurai1, Kulchanat Prasertsit1, Anil Kumar3,4

1Department of Chemical Engineering, Faculty of Engineering, Prince of Songkla University, Songkhla 90112, Thailand. 2Department of Chemical Engineering, Faculty of Chemistry, Quy Nhon University, Binh Dinh 820000, Vietnam.

3Department of Mechanical Engineering, Faculty of Engineering, Prince of Songkla University, Songkhla 90112, Thailand. 4Department of Energy (Energy Center), Maulana Azad National Institute of Technology, Bhopal, India.

*Correspondence Author

Abstract

In the present study, response surface methodology (RSM) and

artificial neural network (ANN) are applied for biodiesel

production via base-catalyzed transesterification. These models

are also compared in order to optimize the methyl esters

production process from edible oils. Methanol/oil molar ratio

(3:1-9:1), sodium methoxide catalyst content (0.50-1.30 wt%),

reaction temperature (45-65oC) and time (30-70 min) were

considered during process using Central Composite Design.

RSM and ANN models show a high accuracy in terms of

coefficient of determination (R2> 0.99) and mean relative

percent deviation (MRPD = 0.22-0.27%). Molar ratio and

catalyst content are identified as two most important factors for

base-catalyzed methanolysis. A high predicted output of

FAME percentage of 98% was determined by the ANN model

under optimum conditions; including MeOH/oil molar ratio of

5.88, catalyst content of 0.89 wt%, reaction temperature of 55 oC in 50 min. Therefore, ANN model is a better solution over

the RSM model and recommended for optimizing biodiesel

production.

Keywords: Biodiesel; Response Surface Methodology;

Artificial Neural Network; Transesterification.

Nomenclature

FAME Fatty acid methyl ester

RSM Response surface methodology

ANN Artificial neural network

CCD Central composite design

DOE Design of experiment

EED Essential experimental design

R Correlation coefficient

R2 Coefficient of determination

MSE Mean square error

RMSE Root mean square error

MAE Mean absolute error

SEP Standard error of prediction

MRPD Mean relative percent deviation

GC Gas chromatography

INTRODUCTION

The development of the world economy is depended on energy

resources. As per the U.S. Energy Administration report of

2016, fossil fuels were the biggest source of energy (78%),

whereas, the nuclear power and renewable energy were only

10% and 12%, respectively [1]. Many environmental

complications like global warming, pollution, ozone layer

depletion are due to fossil fuels [2]. Therefore, the great

challenge is to produce energy from non-fossil and eco-friendly

resources. Biodiesel has proven as a good replacement because

of its renewability, biodegradability, non-toxic and high safety

[3,4].

The most common method for biodiesel production is

vegetable alcoholysis or transesterification [5,6]. In this

method, vegetable oil reacts with alcohol in the presence of

catalyst and create biodiesel and glycerol [5,7]. Base-catalyzed

transesterification method has been studied among the

catalyzed transesterification process by various researchers due

to its high catalytic activity and, higher conversion of

triglyceride to biodiesel [8,9].

Alcohol/oil molar ratio, catalyst content, time and reaction

temperature are factors affect base-catalyzed transesterification

process [2,3,8]. Process optimization is an important and

notable issue and, requires to increase the biodiesel production

efficiency and to reduce the production cost. The base-

catalyzed transesterification process involved in these factors

have been studied, modeled and optimized by RSM and ANN

[8,10-15].

RSM is one of significant statistical method used in

experimental design, modeling and optimization [16,17]. It

gives relation between one or more responses with independent

factors. It also determines the effect of independent factors,

including single effects and interaction effects, on the whole

process. Moreover, this method gives a mathematical relation

for predicting the desire output. Thus, biodiesel can be modeled

from RSM with minor estimation error in different conditions.

Several researchers have been used this tool effectively for the

efficiency evaluation of biodiesel production from base-

catalyzed transesterification [6,18]. Thoai et al. have applied

RSM in the optimization of the one-step methanolysis of

refined palm oil (RPO) catalyzed by sodium methoxide as

homogeneous base catalyst [8]. Moreover, Thoai et al.

continued using RSM in the optimization of the novel two-step



7530

transesterification [12]. RSM has also been used in based-

catalyzed ethanolysis of sunflower oil [13,19].

ANN is the most popular artificial learning tool with a wide

application range. It has been extensively accepted as an

alternative technique to represent the complicated input and

output relationship of the process [20]. It is able to use for

prediction outputs of a new input data, if ring of data is

successfully trained, validated and tested by ANN. It has been

successfully used for several transesterification processes

through based-catalyzed mechanism, including the one-step

and two-step process [11-14]. Betiku et al. have modeled and

optimize the two-step process for biodiesel synthesis from non-

edible neem seed oil. The results demonstrated that the ANN

model accurately represented the process [11]. In another

study, Stamenkovíc et al. showed optimization capability of

ANN in base-catalyzed one-step ethanolysis of sunflower oil

[13]. RSM and ANN were also considered for developing and

comparing their predictive and generalization abilities in the

ethanolysis reaction of refined sunflower oil [13].

RSM and ANN have been applied from long time in order

to model and optimize the alkyl esters production process from

edible oils, however, their results for same study is hardly

compared. The aim of present study is to combine the Central

Composite Design (CCD) with both RSM and ANN

performance for palm oil methanolysis process catalyzed by

homogeneous base catalyst – sodium methoxide. This is first

effort to study the predictive capability evaluation of RSM and

ANN models of the said process.

MATERIALS AND METHODS

Materials

Refined palm oil (RPO) was bought from Morakot Industry

Public Co. Ltd. (Thailand). Methanol (CH3OH, 99%) and

sodium methoxide (CH3ONa, 96%) were supplied by Labscan

Asia Co. Ltd. (Thailand) and Dezhou Long Teng Chemical Co.

Ltd. (China), respectively. Sodium hydroxide (NaOH) was

obtained from Merck (Germany), while sodium periodate

(NaIO4) was acquired from Fisher Chemical (UK) and

bromothymol blue was provided by Ajax Finechem (Australia).

Methods

One-step biodiesel production

The RPO used for this study had the low free fatty acid (FFA)

content (0.11 wt%) which is suitable feedstock oil for one-step

biodiesel production. The catalyzed methanolysis reaction was

carried out in a 0.5 L three-necked flask with magnetic stirring

of 600 rpm at atmospheric pressure, and refluxed by water at

20 oC to condense the methanol vapor. RPO was preheated until

attain the required temperature. Later, the mixture of methanol

and catalyst was added in RPO. The beginning time for the

reaction was recorded at the moment when all of methanol and

catalyst were entered to the reactor. The product mixture was

poured into separatory funnel to separate into two layers of

ester and glycerol after finish this reaction. The settling time

was 60 min. Glycerol was taken out of separating funnel and

the ester phase was washed by hot water (80 oC) for three-three

times without and with shaking. The washed methyl ester was

dried by the heating at 110 oC for 90 min. Finally, the biodiesel

product (FAME) was checked for the ester content.

All the experiments were performed three times to estimate its

errors. Experiments were designed at various conditions;

including MeOH/Oil molar ratio of 3/1-9/1, CH3ONa catalyst

content of 0.50-1.30 wt%, reaction temperature of 45-65 oC and

reaction time of 30-70 min.

Procedure of the ester content determination in biodiesel

Ester content analysis using Gas Chromatography (GC)

Methyl ester content was analyzed by following the standard

method on B-100 biodiesel specified by the Department of

Energy Business, Ministry of Energy, Thailand [21]. This

method is based on European Standard (EN 14103) and was

carried out at Scientific Equipment Center, Prince of Songkla

University, Thailand. The methyl esters were quantified

directly in gas Chromatography (GC) equipped with flame

ionization detector (GC-FID). The column selected for

biodiesel have length 30 m, 0.32 mm internal diameter, film

thickness 0.25 m with helium as the carrier gas at a flow rate

of 1.0 mL/min and split ratio of 50:1. The inlet temperature was

kept at 290 oC and the initial temperature was hold at 210oC

(for 12 minutes) followed by increasing at a rate of 20 oC/min

till 250 oC, hold for 8 minutes. The detector temperature was

kept at 300oC and the injection volume of 1l was used for

analysis. Methyl heptadecanoate was used as the standard of

this analytical method. FAME content, CFAME (%) is calculated

from integration results for a particular determination

according to Eq. (1).

𝐶𝐹𝐴𝑀𝐸 =(∑ 𝐴)−𝐴𝐸𝐼

𝐴𝐸𝐼×

𝐶𝐸𝐼×𝑉𝐸𝐼

𝑚× 100% (1)

where, A is the sum of all methyl ester peaks from C12 to

C24:1, AEI is peak area for methyl heptadecanoate (internal

standard), CEI is concentration (mg/ml) of the methyl

heptadecanoate solution (10 mg/ml), VEI is volume (ml) of the

methyl heptadecanoate solution used (5 ml) and ‘m’ is exact

weight (mg) of the FAME.

Novel chemical method in determining of ester content

In the study of Thoai et al., based on the mechanism of

transesterification, one mole glycerol is produced from one

mole glyceride in a large excess of alcohol and catalyst [22].

From glycerol titration process, the remaining content of

glycerides can be proximate calculated from the content of total

glycerol. Finally, ester content can be converted proximately

by subtracting the content of remaining glycerides from 100

wt%.

Design of experiments

The CCD was applied to investigate the influences of the

experimental variables on the FAME content and to find the

optimum conditions for the requested FAME content. The CCD



7531

incorporates five levels (coded–α, –1, 0, +1, +α) in which axial

points (±α) for a factor and 0 for all other factors. In addition,

the center points code 0 were used to estimate pure error. The

four important factors: MeOH/RPO molar ratio (X1), catalyst

content (X2), temperature (X3) and time (X4) were investigated

as independent variables. The experimental limit and code

levels of independent factors are shown in Table 1. A list of 30

experiments including 24 factorial runs, 8 runs for axial points

and 6 runs for center points were carried out for CCD with 4

independent factors. These experimental FAME contents were

used in the analysis of variance (ANOVA). The performances

of RSM and ANN models are statistical tested by correlation

coefficient (R), coefficient of determination (R2), adjusted R2,

mean square error (MSE), root mean square error (RMSE),

mean absolute error (MAE), standard error of prediction (SEP)

and mean relative percent deviation (MRPD). These

parameters are determined from Eqs. (2) to (9) [13,23,24]:

𝑅 =∑ (𝑦𝑝,𝑖−𝑦𝑝,𝑎𝑣𝑒)(𝑦𝑎,𝑖−𝑦𝑎,𝑎𝑣𝑒)𝑛

𝑖=1

√[∑ (𝑦𝑝,𝑖−𝑦𝑝,𝑎𝑣𝑒)2𝑛

𝑖=1 ][∑ (𝑦𝑎,𝑖−𝑦𝑎,𝑎𝑣𝑒)2𝑛

𝑖=1 ]

(2)

𝑅2 = 1 −∑ (𝑦𝑎,𝑖−𝑦𝑝,𝑖)

2𝑛𝑖=1

∑ (𝑦𝑝,𝑖−𝑦𝑎,𝑎𝑣𝑒)2𝑛

𝑖=1

(3)

𝐴𝑑𝑗𝑢𝑠𝑡𝑒𝑑 𝑅2 = 1 − [(1 − 𝑅2) ×𝑛−1

𝑛−𝑘−1] (4)

𝑀𝑆𝐸 =1

𝑛∑ (𝑦𝑝,𝑖 − 𝑦𝑎,𝑖)

2𝑛𝑖=1 (5)

𝑅𝑀𝑆𝐸 = √1

𝑛∑ (𝑦𝑝,𝑖 − 𝑦𝑎,𝑖)

2𝑛𝑖=1 (6)

𝑀𝐴𝐸 =1

𝑛∑ |(𝑦𝑎,𝑖 − 𝑦𝑝,𝑖)|𝑛

𝑖=1 (7)

𝑆𝐸𝑃 =𝑅𝑀𝑆𝐸

𝑦𝑎,𝑎𝑣𝑒× 100 (8)

𝑀𝑅𝑃𝐷 =100

𝑛∑ |

𝑦𝑎,𝑖−𝑦𝑝,𝑖

𝑦𝑎,𝑖|𝑛

𝑖=1 (9)

where, n is the number of experiments, yp,i is the predicted

outputs, ya,i is the experimental results, ya,ave is the average

experimental results, yp,ave is the average predicted output and k

is the sum of input factors.

Table 1. Limit and code levels of independent factors for the

modeling and optimization from RSM and ANN.

Factor Limit and code level

Independent variable Symbol Dimension –α –1 0 +1 +α

Molar ratio

Catalyst content

Temperature

Time

X1

X2

X3

X4

mol/mol

wt% oC

min

3.00

0.50

45

30

4.50

0.70

50

40

6.00

0.90

55

50

7.50

1.10

60

60

9.00

1.30

65

70

RSM modeling

The four important factors: molar ratio (X1), catalyst content

(X2), reaction temperature (X3) and reaction time (X4), are

investigated as independent variables for modeling and

optimization of FAME content (y). Multiple regressions were

applied for the second-order polynomial regression model

equation in order to find correlation between the response value

and the independent variables. Eq. (10) shows the fitted

quadratic response model.

𝑦 = 𝛽0 + ∑ 𝛽𝑖𝑋𝑖 + ∑ ∑ 𝛽𝑖𝑗𝑋𝑖𝑋𝑗4𝑗=𝑖+1 + ∑ 𝛽𝑖𝑖𝑋𝑖

24𝑖=1

3𝑖=1

4𝑖=1 (10)

where, y is the predicted response (FAME content); β0, βi, βii,

βij are the regression coefficients (β0 is referred to as the

intercept term, βi are linear terms, βii are quadratic terms and βij

are interaction terms); Xi, Xj are coded as independent factors.

The statistical significance of the independent variables, their

interactions and the quality of the fitted model are tested via F-

value, P-value and ANOVA. ANOVA is also applied to predict

the FAME content following the experimental variances.

Contour plots are formed via the multiple regression equation

by keeping two independent terms at an average value while

vary other two terms. Model gives the optimum conditions for

achieving highest-FAME content from independent

experimental factors.

RSM uses Essential Experimental Design (EED) software in

MS Excel [25]. After loading EED, an additional menu option,

DOE (Design of Experiment), is become available in the main

menu of MS Excel (menu Add-Ins). ER (Essential Regression)

software is used for multiple regression and polynomial

regression of experimental data. Additionally, Minitab

software, version 16.2.2 is used to check the accuracy of

results.

ANN modeling

A feed forward, back-propagation multi-layer perception

(MLP) neural network analysis is carried out through the

Levenberg-Marquardt (LM) algorithm for modeling of the

process parameters of the base-catalyzed methanolysis

reaction. This is done by using the neural network toolbox of

MATLAB 2015a (8.5.0.197613). Training parameters of the

ANN are given in Table 2. The MLP network is well known

and widely applied feed forward network analysis. The feed

forward network is a straight forward network that requires

outputs in order to train the model. The ANN operating ability

is investigated by MSE. The selected ANN has three layers of

neurons such as; an input layer, a hidden layer and an output

layer. The hyperbolic tangent sigmoid transfer function

(Tansig) and linear transfer function (Purelin) are chosen for

input and output layers, respectively. The architecture of the

ANN is shown in Figure 1. The sum of input layer neurons are

four, correspond to MeOH/RPO molar ratio (X1), catalyst

content (X2), temperature (X3) and reaction time (X4). The

output layer is FAME content. The optimum hidden neurons

number is found by a heuristic method. It also examines various

numbers of neurons until the MSE of the output data is the

lowest value.



7532

Table 2. ANN parameters used for training, modeling and

optimization of base-catalyzed methanolysis of RPO.

An effective ANN model can be developed if the design terms

and its responses are normalized. The input factors and output

value are normalized before training to eliminate the over

fitting. The input values and output value are normalized as

following equations:

𝑥𝑖,𝑛𝑜𝑟𝑚𝑎𝑙𝑖𝑧𝑒𝑑 =𝑋𝑖𝑗−𝑋𝑖,𝑎𝑣𝑒

0.5(𝑋𝑖,𝑚𝑎𝑥−𝑋𝑖,𝑚𝑖𝑛) (11)

𝑦𝑛𝑜𝑟𝑚𝑎𝑙𝑖𝑧𝑒𝑑 =𝑌𝑗−𝑌𝑎𝑣𝑒

0.5(𝑌𝑚𝑎𝑥−𝑌𝑚𝑖𝑛) (12)

where, xi,normalized: normalized input layer of input variable i; Xij:

the value of input variable i at experimental run j; Xi,ave: the

average value of input variable i; Xi,max and Xi,min: the maximum

and minimum value of input variable i, respectively; ynormalized:

normalized output variable; Yj: the value of output variable at

experimental run j; Yave: the average value of output variable;

Ymax and Ymin: the maximum and minimum value of output

variable, respectively.

Figure 1 Structure of single hidden layer network of ANN in this study.

The output variable (FAME content) of the ANN model is

determined and written as follows:

𝑦𝑛𝑜𝑟𝑚𝑎𝑙𝑖𝑧𝑒𝑑 = 𝑓2(𝑎2) (13)

𝑎2 = (∑ 𝜔𝑗2 × 𝑓1(𝑎𝑗

1)3𝑗=1 ) + 𝑏2 (14)

𝑎𝑗1 = (∑ 𝜔𝑖𝑗

1 × 𝑋𝑖4𝑖=1 ) + 𝑏𝑗

1 (15)

where i: the sum of input terms (i=4); j: the sum of optimum

neurons (j=3); a1 and a2: the linear combined outputs of the

hidden layer and the output layer, respectively; b1 and b2: the

bias of the hidden layer and the output layer, respectively; f1

and f2: the transfer function for the hidden layer and the output

layer, respectively.

Finally, the output value is calculated or de-normalized to the

original units by equation:

𝑦 = (𝑦𝑛𝑜𝑟𝑚𝑎𝑙𝑖𝑧𝑒𝑑 × 0.5 × (𝑦𝑚𝑎𝑥 − 𝑦𝑚𝑖𝑛)) + 𝑦𝑎𝑣𝑒 (16)

where y: output variable; ynormalized: normalized output variable;

ymax and ymin: the maximum and minimum experimental output

variables, respectively; yave: the average experimental output

variable.

As mentioned above, total 30 experiments are completed with

CCD design. Data are separated into three parts, including

training (70% of total data points), testing (15% of total data

points) and validation (15% of total data points) in ANN [24].

In the first, the training data are randomly chosen from the

initial data. The weighted parameters of the interactions are

calculated through a chain of repeats to get the minimum

number of MSE between the calculated values and

experimental FAME content. Subsequently, the testing data are

applied to check the trained ANN. Finally, the validation data

show the prediction of FAME content via the developed ANN

modeling.

Evaluation ability of the RSM and ANN models

The developed models using RSM and ANN are investigated

for predictive ability for the base-catalyzed methanolysis

process. The coefficients of R, R2, adjusted R2, MSE, RMSE,

MAE, SEP and MRPD are determined and employed for this

purpose.

Property Value/comment

Algorithm

Minimized error function Learning

Input layer

Hidden layer

Output layer

Number of best interaction/Epoch

Number of input neurons

Number of hidden neurons

Number of output neurons

Levenberg-Marquardt (LM)

Back propagation (BP)

MSE

Supervised

No transfer function is used

TANSIG

PURELIN

27

4

3

1

x1

x2

x4

x3

𝑓11

𝑓21

𝑓31

𝑓2 y

𝜔211

𝜔111

𝜔121 𝜔13

1

𝜔221

𝜔231

𝜔311

𝜔321

𝜔331

𝜔411 𝜔42

1

𝜔431 𝑏3

1

𝑏21

𝑏11

𝑎11

𝑎21

𝑎31

𝜔12

𝜔22

𝜔32

𝑏2

𝑎2

normalized

normalized

normalized

normalized

normalized

Input Hidden layer Output



7533

RESULTS AND DISCUSSIONS

The relationship between the four independent variables

(MeOH/RPO molar ratio, catalyst content, reaction

temperature and reaction time) and the FAME content is

determined. The FAME content for each experimental run and

from both RSM and ANN models are listed in Table 3.

RSM modeling

Analysis of variance (ANOVA)

Results of ANOVA in terms of the degree of freedom, the

sum and means of squares, F-value and P-value are given in

Table 4. The significance of the model, single terms, their

squares and interactions is confirmed via their F-value and P-

value. P-value less than 0.05 imply significant effects of these

parameters on the FAME content.

Table 3. Designed independent factors and experimental results.

Run

No.

Independent variables/ Input variables Output variable/ FAME content (%)

X1 (mol/mol) X2 (wt%) X3 (oC) X4 (min) Experiment RSM model ANN model

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

4.50

7.50

4.50

7.50

4.50

7.50

4.50

7.50

4.50

7.50

4.50

7.50

4.50

7.50

4.50

7.50

3.00

9.00

6.00

6.00

6.00

6.00

6.00

6.00

6.00

6.00

6.00

6.00

6.00

6.00

0.70

0.70

1.10

1.10

0.70

0.70

1.10

1.10

0.70

0.70

1.10

1.10

0.70

0.70

1.10

1.10

0.90

0.90

0.50

1.30

0.90

0.90

0.90

0.90

0.90

0.90

0.90

0.90

0.90

0.90

50

50

50

50

60

60

60

60

50

50

50

50

60

60

60

60

55

55

55

55

45

65

55

55

55

55

55

55

55

55

40

40

40

40

40

40

40

40

60

60

60

60

60

60

60

60

50

50

50

50

50

50

30

70

50

50

50

50

50

50

83.51

94.48

90.60

98.64

86.87

95.31

93.42

98.83

85.76

96.28

91.56

98.74

87.92

95.59

93.34

98.78

80.84

98.45

87.07

97.53

93.45

95.92

93.61

96.21

94.87

95.32

95.19

94.79

94.47

95.04

MSE

R2

83.29

94.45

90.32

98.59

86.39

95.11

93.21

99.05

85.55

96.20

91.47

99.23

87.67

95.88

93.38

98.70

81.55

98.03

87.52

97.37

93.54

96.12

94.10

96.01

94.95

94.95

94.95

94.95

94.95

94.95

0.0879

0.9953

83.29

94.56

90.64

98.02

86.80

96.13

92.99

98.61

85.78

96.27

91.82

98.68

88.05

95.59

93.80

98.80

81.06

98.37

87.02

97.57

93.50

96.23

94.14

96.24

94.82

94.82

94.82

94.82

94.82

94.82

0.0010

0.9958

From Table 4, molar ratio (X1), catalyst content (X2), reaction

temperature (X3), reaction time (X4) and square terms of molar

ratio and catalyst content (X12, X2

2) have positive effects on the

FAME content. Moreover, two-way interaction of molar ratio



7534

with catalyst content and reaction temperature (X1X2, X1X3),

catalyst content and reaction time (X2X4), reaction temperature

and time (X3X4) also have statistically significant effects on the

FAME content. However, in other terms, X32, X4

2, X1X4 and

X2X3 are observed to be insignificant on the FAME content.

The important operational variables molar ratio, catalyst

content, temperature and reaction time and have F-values of

2318.83, 828.49, 56.45 and 31.41, respectively, and P-value

<0.0001 (Table 4). Molar ratio and catalyst content have very

high F-value as compared to other individual variables. This

means that the molar ratio and catalyst content are the two most

important factors in the present study. The increases the

methoxide anion concentration speed up the FAME formation

rate. This shows importance of the MeOH/RPO molar ratio in

the enhancement the forward reaction rate. It shifts the reaction

equilibrium toward the formation of product at higher

concentration of methanol. The present results are similar to

previous researches which shows the effects of molar ratio and

catalyst content for base-catalyzed methanolysis [15,26].

Table 4. Results of ANOVA.

Source/ Term Degree of

freedom (DF)

Sum of

squares (SS)

Mean square

(MS)

F–value P–value Remarks

Model

Linear

X1

X2

X3

X4

Square

X12

X22

X32

X42

2-Way interaction

X1X2

X1X3

X1X4

X2X3

X2X4

X3X4

Residual

Lack of Fit (LOF)

Pure Error

Total

14

4

1

1

1

1

4

1

1

1

1

6

1

1

1

1

1

1

15

10

5

29

639.242

568.491

407.468

145.583

9.920

5.520

54.002

45.592

10.732

0.024

0.020

16.749

8.309

5.941

0.263

0.043

1.238

0.956

2.636

2.171

0.465

641.878

45.660

142.123

407.468

145.483

9.920

5.520

13.500

45.592

10.732

0.024

0.020

2.792

8.309

5.941

0.263

0.043

1.238

0.956

0.176

0.217

0.093

259.84

808.79

2318.83

828.49

56.45

31.41

76.83

259.46

61.07

0.13

0.11

15.89

47.28

33.81

1.49

0.25

7.04

5.44

2.33

<0.0001

<0.0001

<0.0001

<0.0001

<0.0001

<0.0001

<0.0001

<0.0001

<0.0001

0.720

0.741

<0.0001

<0.0001

<0.0001

0.240

0.628

0.018

0.034

0.181

Significant

Significant

Significant

Significant

Significant

Significant

Significant

Significant

Significant

Not significant

Not significant

Significant

Significant

Significant

Not significant

Not significant

Significant

Significant

Not significant

R2 = 0.9953, adjusted R2 = 0.9929, R2 for prediction = 0.9842



7535

Prediction of FAME content by RSM

FAME content in the final biodiesel product is strongly

influenced by four operational variables. From Table 3, the

initial regression model is shown in Eq. (17):

𝑌 = −42.86 + 16.68𝑋1 + 64.68𝑋2 + 1.036𝑋3 + 0.466𝑋4 −0.573𝑋1

2 − 15.64𝑋22 − 0.00117𝑋3

2 + 0.000270𝑋42 −

2.402𝑋1𝑋2 − 0.08125𝑋1𝑋3 − 0.00854𝑋1𝑋4 −0.05187𝑋2𝑋3 − 0.139𝑋2𝑋4 − 0.00489𝑋3𝑋4 (17)

The fit of the designed model is checked as per F-value, P-

value, lack of fit error (LOF), R2, adjusted R2 and R2 for

prediction [8,17,18]. The model’s F-value 259.84 and the very

low P-value (<0.0001) indicates that the corresponding model

is noteworthy (Table 3). The LOF of 0.181 (much higher 0.05)

implies that LOF is meaningful relative to the pure error [8].

Pointless LOF is good for predicted model. Additionally, in the

evaluation the importance of the suggested model, large

differences between R2, adjusted R2 and predicted R2 also

demonstrate the significance of the model [17,18]. These

coefficients (R2, adjusted R2, predicted R2) are very high

(0.9953, 0.9929 and 0.9824, respectively) and prove the worth

of the model (Table 4).

Correlation is linear and most of experimental points are

located on the 45-degree line as depicted in Figure 2. Therefore,

the suggested model is precise description of the process.

Figure 2 Comparison of predicted and experimental FAME

content.

The final practical model based on the coded factor, ANOVA

data and by eliminating the irrelevant model terms is given in

Eq. (18):

𝑌 = −34.86 + 16.25𝑋1 + 61.82𝑋2 + 0.86𝑋3 + 0.442𝑋4 −0.573𝑋1

2 − 15.63𝑋22 − 2.402𝑋1𝑋2 − 0.08125𝑋1𝑋3 −

0.139𝑋2𝑋4 − 0.00489𝑋3𝑋4 (18)

ANN modeling

Development of ANN

The FAME content is predicted based on the ANN with LM

algorithm includes four input layer neurons and one output. The

ANN model depends on the decisive optimum neuron numbers.

The influence of the sum of neurons in the hidden layer is

investigated in order to determine the optimum neurons. This

process consists of examine the chain of various neurons until

the MSE are the lowest value. The number of neurons is varied

from 1 to 25. Results for the ANN model are shown in Figure

3. The optimum sum of neurons for the ANN model is 3

neurons with the minimum MSE of 0.00097664 (Figure 4).

Initially high MSE reduced rapidly to a smallest value. The

MSE depends on the number of neurons of ANN model and are

shown in Table A (Appendix). Table B in Appendix also shows

weights, bias and the transfer functions for the ANN model

with 2 layers and 3 optimum neurons.

Figure 3 Validation MSE response for the ANN model.

Figure 4 MSE values for training, validation and testing of

the developed ANN model.

Prediction of FAME content by ANN

Fig. 5 compares the predicted and actual FAME content for

training (R = 0.99881), validation (R = 0.9986), testing (R =

0.95991) and the overall regression (R = 0.99795) of the

developed ANN model as per the 4-3-1 configuration (4 input

variables, 3 neurons in hidden layer and 1 output variable).

Most data points are distributed on the 45-degree line which

shows a very good mutual relationship between the

experimental data and predicted outputs. Results also confirm

the developed ANN model is absolutely agreed to predict the

output values of the validation and testing data.



7536

Figure 5 Comparisons of the predicted and experimental FAME content (output) for training (a), validation (b), testing (c) and the

overall regression (d) for 3 neurons.

Predictive capability of RSM and ANN models

The capability of the developed RSM and ANN models in

prediction of the FAME content in biodiesel is evaluated in

terms of their R, R2, adjusted R2, mean square error (MSE), root

mean square error (RMSE), mean absolute error (MAE),

standard error of prediction (SEP) and mean relative percent

deviation (MRPD). These results are presented in Table 5. If

the value of the R is close to 1 then there is a good correlation

between experimental and predicted values. The two models

have very high values of R2, demonstrate the authentic

suitability of these models [24]. The adjusted R2 is used in

testing over fitting of R2. These are also high for the two models

which, the models. Moreover, the RMSE – the square root of

the MSE – is also determined for both models. MSE value from

ANN model (0.0010) is much lower as compared to RSM

model (0.0879). The similar difference is also obtained for

RMSE, with 0.0313 and 0.2964, respectively. Results confirm

the ANN model is better than the RSM model (Table 5). MAE,

SEP and MRPD check the significance and accuracy of the

models [23,24,27]. The lower values of these statistical

parameters, better the performance of the model.

Table 5. Performance evaluation of RSM, ANN models.

Parameter RSM ANN

R

R2

Adjusted R2

MSE

RMSE

MAE

SEP (%)

MRPD (%)

0.9979

0.9953

0.9921

0.0879

0.2964

0.2448

0.3173

0.2667

0.9980

0.9958

0.9903

0.0010

0.0313

0.0233

0.0335

0.2232

Several studies have shown that ANN is better than RSM

model in prediction capability [13,23,24,27-29]. Further, these

results have not proven the difference between MSE and RMSE

for the RSM and ANN models. The present study has passed

this difficulty and contributes a fully confirmation about the

effectiveness of the developed ANN and compared to the RSM

model.



7537

Optimization of FAME content by the RSM and ANN

models

Actual FAME content under the experimental conditions are

between 80% to 100% (Fig. 2). In order to evaluate the

optimization capability of the RSM and ANN models, the

FAME content of 96.5% and 98% were chosen as a desired

target of base-catalyzed methanolysis. The optimum condition

for temperature and reaction time are same for both models

with regard to same desired target (Table 4). In a contrary, the

optimum molar ratio and catalyst content from these models

have a remarkable difference. The molar ratio and catalyst

content are the two most important factors for base-catalyzed

methanolysis in the present study as per ANOVA results (Table

4). Therefore, the evaluation for the RSM and ANN models is

as per these two important factors. The values of molar ratio

and catalyst content required for base-catalyzed FAME

synthesis by ANN model are lower in comparison with RSM

model (Table 6). Thus, ANN model is better in prediction

capability as compare to RSM model.

Table 6. Optimization conditions and model validation.

Model RSM ANN

96.5 % FAME 98% FAME 96.5 % FAME 98% FAME

MeOH/RPO molar ratio

CH3ONa content (wt%)

Reaction temperature (oC)

Reaction time (min)

6.15

1.01

55

50

7.57

1.20

55

50

5.49

0.87

54.7

49.8

5.88

0.89

54.9

50

To check the validation of RSM and ANN models, triplicate

experiments were repeated under the predicted optimum

conditions from each model with the same target of the ester

content (98%). Table 7 shows the experimental value of the

ester content in final biodiesel production. The experimental

ester content value obtained from ANN is in close agreement

with the suggested target. As a result, ANN proved to be more

effective than RSM in optimizing the biodiesel production in

the present study.

Table 7. The validation of RSM and ANN models with the

ester content of 98% as a target.

Model Molar

ratio

(mol/mol)

Catalyst

content

(wt%)

Temperature

(oC)

Time

(min)

Ester

content

from

experiment

(%)

RSM 7.57 1.20 55 50 99.64

ANN 5.88 0.89 54.9 50 97.95

CONCLUSION

RSM and ANN models were developed and compared for their

predictive and generalization abilities in the methanolysis

process of palm oil catalyzed by sodium methoxide in the

present study. Following conclusions are drawn:

1. The predictive capability of the two models for sodium

methoxide-catalyzed methanolysis was compared using

the same experimental conditions from the CCD.

2. High values of R, R2, predicted R2 (> 0.99) clearly

indicates high accuracy of both RSM and ANN models.

3. Both models have proven the important role of the molar

ratio and catalyst content for base-catalyzed

methanolysis.

4. Earlier, the difference of the predictive capability

between RSM and ANN is only based on R2, adjusted R2

and R2 for prediction, this may be the first study in

evaluating in terms of MSE, RMSE, MAE, SEP, and

MRPD.

5. Lower values of the ANN models demonstrated that the

ANN model is a better choice compared to the RSM

model by paying attention to parameters (MSE, RMSE,

MAE, SEP, MRPD) and recommended for similar

studies.

ACKNOWLEDGEMENTS

This research work was supported by Graduate School of

Prince of Songkla University under Thailand’s Education Hub

for ASEAN Countries (Contract No.: TEH-AC 047/2014).



7538

APPENDIX A

Table A. Mean square error (MSE) depends on the number of neurons of ANN model.

Number of

neurons

MSE Number of

neurons

MSE Number of

neurons

MSE

1 0.0092157 10 0.0112460 18 0.0367090

2 0.0059002 11 0.2336700 19 0.1121600

3 0.0009766 12 0.0815890 20 0.0527680

4 0.0251790 13 0.0297210 21 0.0875460

5 0.0034538 14 0.0638450 22 0.1693700

6 0.0294600 15 0.4596200 23 0.0871460

7 0.0361070 16 0.0922340 24 0.3110600

8 0.0113680 17 0.1307600 25 0.0621300

9 0.0163470

APPENDIX B

Table B. Weights, bias and transfer function of ANN model (optimum neurons: 3)

Weights 1st layer Weight size for 1st layer Bias Size [3x1] Transfer function

𝑤1,11 -1.3116 𝐵1

1 2.8172 𝑓11 = 𝑡𝑎𝑛ℎ

𝑤1,21 0.84862 𝐵2

1 1.0268 𝑓21 = 𝑡𝑎𝑛ℎ

𝑤1,31 0.45611 𝐵2

1 -3.4715 𝑓31 = 𝑡𝑎𝑛ℎ

𝑤2,11 2.1058

𝑤2,21 0.39497

𝑤2,31 -0.97206

𝑤3,11 0.23611

𝑤3,21 0.173670

𝑤3,31 -1.5561

𝑤4,11 -0.45005

𝑤4,21 0.069986

𝑤4,31 1.7798

Weights 2nd layer Weight size for 2ndlayer Bias Size [1x1] Transfer function

𝑤12 0.88161 𝐵2 -0.77158 𝑓2 = 1

𝑤22 2.5727

𝑤32 1.5377

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predictive capability evaluation of rsm and ann in ...complications like global warming, pollution,...

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